Describing, understanding and controlling the quantum dynamics of molecular systems remains one of the central challenges in modern theoretical and computational science with wide-ranging applications in fields such as photochemistry, ultrafast spectroscopy, strong-field physics, material science, and quantum information science. The increasing availability of high-intensity, short-pulsed laser sources such as laboratory-based high-harmonic generation systems and large-scale, facility-based free-electron lasers has enabled the development of ultrashort laser pulses, reaching femtosecond and even attosecond durations allowing to observe the electronic and nuclear motion on their intrinsic timescales. These developments open unprecedented opportunities for real-time observation of fundamental processes, including e.g. charge migration, bond cleavage, and energy redistribution. To interpret the rich information provided by such experiments, advanced theoretical frameworks are essential. In particular, quantum dynamics (QD) simulations based on solving the time-dependent Schrödinger equation (TDSE) are indispensable for linking experimental observables to the underlying molecular behavior. 

Over the last two decades there have been huge advances in QD methods, with grid-based algorithms such as multi-configurational time-dependent Hartree (MCTDH),[1] trajectory based methods such as Surface Hopping [2] and Gaussian Wavepacket based methods [3] such as Multiple Spawning [4] becoming commonly used. There are also now open source software packages implementing these methods available to the community.[5] However, the accurate and efficient simulation of systems of interest remains highly demanding, due to the large number of degrees of freedom and the complexity of the interactions involved. Problems due to numerical instabilities, integration errors and conservation of properties such as energy and norm are also common. Addressing these challenges calls for close collaboration between physicists, chemists, mathematicians, and computer scientists, in order to develop novel theoretical methods and computational tools capable of capturing quantum dynamics with both accuracy and scalability. There is already a growing body of successful joint work between mathematicians and theoretical chemists developing quantum dynamics methods, demonstrating the value of interdisciplinary collaboration in tackling complex challenges in this area.[6-9]

This alternative CECAM workshop aims to bring together computational and theoretical chemists with applied mathematicians specialisingin numerical analysis and scientific computing. The goal is to foster mutual understanding, encourage collaboration, and inspire advancements in numerical methods for quantum dynamics in chemistry. To establish a shared foundation, we will cover essential topics such as the principles of spectroscopy, observables, representations of nuclear motion, vector space theory, error analysis and propagation. Particular emphasis will be placed on bridging disciplinary language barriers which prevent the uptake of ideas between the communities. The workshop will also explore key themes from both mathematical and chemical perspectives, including the variational principle, spectral methods, tensor contraction, semiclassical techniques, and the use of Gaussian basis functions. By bringing together a diverse range of expertise, we aim to help in particular early career researchers broaden their horizons and to stimulate long-lasting collaborations between the fields to help drive progress in quantum dynamics methods for chemical applications.